A representation of a reservoir or parts of a reservoir by computational means is an important tool for the hydrocarbon producing industry. Reservoir models are used to determine important steps in the development and production of reservoirs. The reservoir model can be seen as an interpreted and specifically formatted representation of the knowledge of the geology and petrophysical properties of the reservoir.
The commonly accepted building process and use of reservoir models includes the steps of creating first a fine-scale, detailed 3D representation of the geological objects in the volume of interest (layers, faults, etc.) and of their petrophysical properties (the geological model). This fine scale model is then typically converted into a coarser scale representation, the so-called simulation model, with its associated petrophysical properties by the way of an upscaling process. The coarse scale representation is then used for example as input for a flow simulator that computes the movements of fluid and the evolution of pressures, saturation of phases and concentrations of elements over time.
A reservoir model typically combines generic knowledge derived from general geological processes such as basin formation, deposition, diagenesis and the like with knowledge specific to the reservoir. Knowledge of the geological objects within a specific reservoir can be gained primarily from reservoir surveys covering large sections of the reservoir. Reservoir survey methods include seismic or electromagnetic surveys. The results of these primary surveys are then augmented by localized survey methods covering the vicinity of wells drilled into the reservoir. Well survey methods include the plethora of well logging methods, seismic profiling, analysis of core and cuttings, flow testing and many more. The combination of the results of reservoir surveys and localized surveys into a common frame or format of representation provides the basis for a fundamental reservoir model.
However this fundamental reservoir model (representing only the measured and interpreted data) is of limited use unless populated more densely and uniformly by interpolation and statistical methods. These methods are employed to fill gaps and associate each grid cell, which is typically the smallest unit of the mathematical description of the model, with formation properties as derived from the limited number of measurements available. It can be easily seen that this step of populating the reservoir model with interpolated or otherwise calculated parameters has the effect of vastly increasing the accuracy of the predictive capacities of the model but at the cost of increased computational resources as relating for example to data storage space and processing speed.
When defining a reservoir model, its primary geometric features or building blocks are the layers or horizons and faults, which when combined define the major segments of the reservoir from a geological point of view. But under these large scale features there are other important geological features which can have a profound impact on the fluid flow through the reservoir. One of the more important of these smaller scale features are fractures, which can be regarded as faults with little or no sliding or slip movement between the fault faces.
It is immediately obvious that the number, the size and the orientations of the fractures within a block can heavily influence the overall permeability of that block to fluid flow, potentially overriding other factors such as rock permeability and porosity, wettability etc. The ability to include an accurate discrete or statistical representation of fractures is therefore generally regarded as a very important aspect within the larger task of building a reservoir model.
When modeling the impact fractures can have on the reservoir, the fractures are most often represented by way of a discrete fracture network (DFN) in the geological model, while they are represented by their effective petrophysical properties in the (coarser) simulation model. This conventional approach is described for example in: B. Bourbiaux, R. Basquet, J. M. Daniel, L. Y. Hu, S. Jenni, A. Lange, and P. Rasolofosaon, “Fractured Reservoirs Modelling: a review of the challenges and some recent solutions”, First Break, vol. 23, pp 33-40, September 2005. A discrete fracture network is a representation in which each individual fracture is represented by a small surface patch (in 3D) or a small polygonal line (in 2D) associated with individual geometrical and petrophysical attributes such as aperture, transmissivity, etc.
The main problem associated with the use of the discrete fracture network representation is that both the memory required to store the DFN representation and the time required to compute the corresponding effective petrophysical properties increase with the number of fractures in the network. The effective petrophysical properties are those quantities which describe the impact of fractures on the physical properties of rocks (e.g. porosity and permeability) at a coarser scale. These properties are commonly assigned to the elementary blocks or volumes of rocks (the grid cells) that, together, form a partition of the volume of interest (the grid).
Several solutions have been proposed to overcome the computational limitations associated with DFN models. All these solutions rely on a simplification of the geological model, and result in a degradation of the corresponding simulation model.
The most popular method, as described for example in: R. Basquet, C. E. Cohen and B. Bourbiaux, “Fracture Flow Property Identification: An Optimized Implementation of Discrete Fracture Network Models”, Proc 14th MEOS, 2005, or in: Daly and D. Mueller, “Characterization and Modeling of Fractured Reservoirs: Static Model”, Proc. ECMOR, 2004 uses instead of a full 3D model a reduced 2.5D model (i.e. a layered 2D fracture network). While this method greatly reduces both computational time and required memory, 2D models provide a poor representation of non layer-bound fractures and cannot model properly fracture basements. Garcia et al. in: M. Garcia, F. Gouth and O. Gosselin, “Fast and Efficient modeling and conditioning of naturally fractured reservoir models using static and dynamic data”, Europec/EAGE ACE, 2007 use a local 2.5D periodic model to represent the detailed fracture network while minimizing the computational cost. While it allows modeling accurately complex relationships between fracture sets, it assumes the existence of a representative elementary volume and may lead to a poor representation of large scale fractures.
Another technique uses the DFN only for local models, in the vicinity of the wells, and interpolates the upscaled effective properties to obtain the full-field model. The disadvantage of these methods is that they do not allow for controlling correctly the model variability in the inter-well space. Basquet et al. as cited above propose to upscale the fine-scale DFN to a coarser discrete model with similar flow behavior. However, the loss of physical realism that is due to the upscaling makes it impossible to validate the quality of the coarse model.
An alternative solution to describing the fractures as DFN is to omit it entirely and use directly an effective medium model as demonstrated in: S. Suzuki, C. Daly, J. Caers, D. Mueller, “History Matching of Naturally Fractured Reservoirs Using Elastic Stress Simulation and Probability Perturbation Method”, Proc. SPE ATCE, 2005 and S. A. Christensen, T. E. Dalgaard, A. Rosendal, J. W. Christensen, G. Robinson, A. M. Zellou, T. Royer, “Seismically Driven Reservoir Characterization Using and Innovative Integrated Approach: Syd Arne Field”, Proc. SPE ATCE, 2006. Suzuki et al. compute directly the permeability from the fracture density, assuming a power-law correlation with the distance to the percolation threshold. This method does not take into account the actual geometry of the fracture network and assumes that all the flowing fractures are locally aligned in the same direction. Christensen et al. use a similar approach, relying on 3D fracture density maps derived from seismic attributes and structural attributes. However, the fracture geometry is not fully described by the geological fracture model and the authors do not propose any explicit method to upscale its permeability.
Finally, some authors, such as Lee, S. H., M. F. Lough, and C. L. Jensen (2001), “Hierarchical Modeling of Flow in Naturally Fractured Formations with Multiple Length Scales”, Water Resour. Res., 37(3), pp. 443-455, use a mixed representation combining large discrete fractures with an effective representation of the medium. But this mixed representation is restricted to the coarse simulation model, and a DFN is still required to compute the properties of the effective properties.
In the light of the known methods it is seen as an object of the present invention to provide a novel method of representing fractures in a reservoir model and modeling accurately the heterogeneity, spatial variability, anisotropy and uncertainty attached to the effective petrophysical properties derived therefrom while minimizing the memory space required by the numerical data structures used for representing the fracture network and maximizing the speed of the algorithms used for computing these.